Abstract
The Schrödinger equation is solved for the truncated Gaussian potential barrier using a power series solution and a general expression is obtained for the transmission coefficient. For this potential barrier, computer calculations show only a trace of the oscillatory behavior that characterizes the penetration of a rectangular barrier. The oscillations diminish rapidly as the discontinuity in the potential function approaches zero. The results indicate that it is the unrealistic discontinuities in potential models that cause such oscillatory behavior.
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